Work

A local-to-global inequality for spectral invariants and an energy dichotomy for Floer trajectories

Year: 2024

Type: article

Abstract: We study a local-to-global inequality for spectral invariants of Hamiltonians whose supports have a “large enough” disjoint tubular neighborhood on semipositive symplectic manifolds. As a corollary, we deduce this inequality for disjointly supported Hamiltonians that are $$C^0$$ C 0 -small (when fixing the supports). In particular, we present the first examples of such an inequality when the Hamiltonians are not necessarily supported in domains with contact-type boundaries, or when the ambient manifold is irrational. This extends a series of previous works studying locality phenomena of spectral invariants [9, 13, 15, 20, 25, 27]. A main new tool is a lower bound, in the spirit of Sikorav, for the energy of Floer trajectories that cross the tubular neighborhood against the direction of the negative-gradient vector field.

Source: Journal of Fixed Point Theory and Applications

DOI: 10.1007/s11784-024-01154-3

Authors: Lev Buhovsky, Shira Tanny

Institutions: Tel Aviv University, Weizmann Institute of Science

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Schmidt Futures, Weizmann Institute of Science, Israel Science Foundation, H2020 European Research Council